We show that Picard–Fuchs equations of periods of certain families of abelian surfaces with quaternionic multiplication have fractional powers of algebraic modular forms as solutions. We give several applications of this modularity property, including a computation of exceptional sets of certain transcendental functions.

中文翻译：

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Q上Shimura曲线的Picard–Fuchs方程

我们证明，具有四元数乘法的某些阿贝尔曲面族的周期的Picard-Fuchs方程具有代数模数形式的分数幂作为解。我们给出了这种模块化属性的几种应用，包括某些超越函数的例外集的计算。